A gambler presents you with an even-money wager. You will roll two dice, and if the highest number showing is one, two, three or four, then you win. If the highest number on either die is five or six, then she wins. Should you take the bet?
Instead of six possibilities, there are now 36. You can make a simple grid to see your odds of winning, with the six possible results for the first die forming the columns, and the six possible results for the second die forming the rows. As you can see, your odds of winning are 16 out of 36, or 4/9, so you should not take the bet.
Remember, if a five or a six shows on either die, the gambler wins. So with two dice, you have to win on both at once, which is harder. The odds of winning with one die are 2/3, so another way to figure the odds of winning on both dice at once is to multiply the probabilities: 2/3 times 2/3 equals 4/9.
This is wrong. Increasing the number of die actually increase your odds and decrease the gambler’s odds percentage of winning.
This puzzle is certainly trickier than it seems. The way the wager is phrased, if there is a 5 or a 6 on either die, the gambler wins. With two dice, the gambler will win about 5 out of 9 rolls. If you don’t believe it, you can test it with real dice.
You’re not too smart, are ya? 1 dice, your odds are 2/3. 2 dice, your odds are 4/9. 3 dice, your odds are, 8/27. Aka your statement is dead wrong and actually backwards. This is because to win the bet, you need to win all the dice involved.
This is wrong
Nope. If you don’t believe it, try it with real dice! Remember, with two dice you have to win on both of them, which lowers the probability. Think of it this way: if you flip one coin, you have a 1/2 chance of getting heads. If you flip two coins, you only have a 1/4 chance of getting heads on both of them.
Extend it further if you wish. The gambler presents you with four dice, and you win if the highest number is 1,2,3,4 or 5! She wins if the highest number is six. Fancy the bet? How confident are you?
Do not take the bet you have a 2/3 chance of losing getting a five or six on the first roll is 33% times 2 because of the second roll is 66% total chance of losing
Don’t take the bet because of two reasons: 1.) You have a 44.44% chance of winning while she has a 55.56% chance of winning. PuzzleWocky has provided the corresponding probability distribution; 2.) This is a zero-sum game. (If you have studied game theory, you would know what is a zero-sum game.) A zero-sum game is simply a game wherein a player can win something only by causing another player to lose the equivalent. So, in a zero-sum game involving two players, both players would breakeven if both of them have a 50-50 chance of winning.
The probability for 1-4 being the highest is 16/36. The probability of having 5 or 6 being highest is 20/36. So the gambler has the best probability of winning.